Dislocation Dynamics During Plastic Deformation (eBook)

Dislocation Dynamics During Plastic Deformation 4
Part I General Properties of Dislocation Motion 14
1 Introduction 15
1.1 Theoretical Yield Strength 16
1.2 Plastic Shear by the Motion of Dislocations 17
2 Experimental Methods 22
2.1 Macroscopic Deformation Tests 22
2.2 Stress Pulse Double Etching Technique 27
2.3 Transmission Electron Microscopy 29
2.4 In Situ Straining Experiments in the Transmission Electron Microscope 31
2.5 Other Methods 37
2.5.1 X-Ray Topography In Situ Deformation Experiments 38
2.5.2 Surface Studies of Slip Lines 38
2.5.3 Internal Friction 40
2.5.4 Nuclear Magnetic Resonance 44
3 Properties of Dislocations 46
3.1 Geometric Properties 46
3.1.1 Burgers Vector 46
3.1.2 Glide and Climb Motion of a Dislocation 48
3.1.3 Relation Between Dislocation Motion and Plastic Strain and Strain Rate 50
3.2 Elastic Properties of Dislocations 51
3.2.1 Stress Fields of Straight Dislocations 52
3.2.2 Dislocation Energy 54
3.2.3 Forces on Dislocations 58
3.2.4 Interaction Between Parallel Dislocations 61
3.2.5 Interaction Between Nonparallel Dislocations 63
3.2.6 Elastic Interaction Between Dislocations and Elastic Inclusions 65
3.2.7 Bowed-Out Dislocations 68
3.3 Dislocations in Crystals 76
3.3.1 Selection of Burgers Vectors 77
3.3.2 Stacking Faults and Partial Dislocations 77
3.3.3 Twins 81
3.3.4 Antiphase Boundaries 82
4 Dislocation Motion 84
4.1 Thermally Activated Overcoming of Barriers 85
4.2 Lattice Friction 89
4.2.1 Peierls–Nabarro Model 90
4.2.2 Double-Kink Model 94
Elastic Properties of Kinks 94
Kinks in Thermal Equilibrium 96
Thermally Activated Motion of Kinks 97
Double-Kink Nucleation at High Stresses 99
Dislocation Velocity in the Range of Double-Kink Nucleation 101
4.2.3 Characteristics and Experimental Evidence of the Double-Kink Model 103
4.3 Slip and Cross Slip 104
4.4 The Locking–Unlocking Mechanism 110
4.5 Overcoming of Localized Obstacles 112
4.5.1 Friedel Statistics 114
4.5.2 Mott Statistics 121
4.6 Transition from the Double-Kink Mechanism to the Overcoming of Localized Obstacles 124
4.7 Overcoming of Extended Obstacles 127
4.8 Dislocation Intersections 137
4.9 Dislocation Motion at High Velocitiesand Low Temperatures 140
4.10 Dislocation Climb 143
4.10.1 Point Defect Equilibrium Concentrations 143
4.10.2 Climb Forces 145
Force Required for Athermal Climb 145
Applied Climb Forces 146
4.10.3 Emission- or Absorption-controlled Climb 148
4.10.4 Diffusion-controlled Climb 151
4.10.5 Jog Dragging 152
4.11 Drag Forces due to Point Defect Atmospheres 154
4.12 Dynamic Laws of Dislocation Mobility 161
5 Dislocation Kinetics, Work-Hardening, and Recovery 166
5.1 Dislocation Kinetics 166
5.1.1 Models of Dislocation Generation 167
5.1.2 Experimental Evidence of Dislocation Generation 173
5.1.3 Dislocation Immobilization and Annihilation 177
5.2 Work-Hardening and Recovery 182
5.2.1 Work-Hardening Models 183
5.2.2 Thermal and Athermal Componentsof the Flow Stress 191
5.2.3 Experimental Determinationof the Stress Components 198
5.2.4 Steady State Deformation 203
5.3 Plastic Instabilities 207
Part II Dislocation Motion in Particular Materials 213
Comments on the Video Sequences Available in the Internet 214
6 Semiconductors 216
6.1 Crystal Structure and Slip Geometry 216
6.2 Microscopic Observations 218
6.3 Dislocation Dynamics 222
6.4 Recombination-enhanced Dislocation Mobility 226
6.5 Macroscopic Deformation Properties 227
6.6 Summary 229
7 Ceramic Single Crystals 230
7.1 Alkali Halides 230
7.1.1 Crystal Structure and Slip Geometry 231
7.1.2 Dislocation Dynamics 232
7.1.3 Macroscopic Deformation Properties 232
7.1.4 Summary 238
7.2 Magnesium Oxide 240
7.2.1 Microscopic Observations 240
7.2.2 Statistics of Overcoming Localized Obstacles 243
7.2.3 Kinematics of Overcoming Localized Obstacles 248
7.2.4 Dislocation Dynamics 251
7.2.5 Macroscopic Deformation Properties and Discussion 252
7.2.6 Dislocations in the Plastic Zone of a Crack 258
7.2.7 Summary 261
7.3 Zirconia Single Crystals 262
7.3.1 Crystal Structure and Slip Geometry of ZrO2–Y2O3 alloys 262
7.3.2 Microscopic Observations in Cubic ZrO2 263
7.3.3 Dislocation Dynamics in Cubic ZrO2 269
7.3.4 Macroscopic Deformation Properties of Cubic ZrO2 270
7.3.5 Deformation Mechanisms 272
The Athermal Stress Component 272
Elastic Interactions Between Dislocations and Point Defects 274
Precipitation Hardening 275
The Peierls Mechanism 276
Formation of Solute Atmospheres Around Dislocations 277
Recovery Controlled Deformation at High Temperatures 279
7.3.6 Summary of Cubic ZrO2 282
7.3.7 Tetragonal ZrO2 282
Microstructure 283
Ferroelastic Deformation 283
Plastic Deformation 285
Partially Stabilized Zirconia 287
Summary of Tetragonal Zirconia 289
8 Metallic Alloys 290
8.1 Precipitation Hardened Aluminium Alloys 290
8.1.1 Al–Zn–Mg 291
8.1.2 Al–Ag 294
8.1.3 Al–Li 296
8.1.4 Summary 302
8.2 Dislocation Generation in Metals 302
8.3 Oxide Dispersion Strengthened Materials 306
8.3.1 Microscopic Observations in Oxide Dispersion Strengthened Alloys 307
8.3.2 Macroscopic Deformation Properties 312
8.3.3 Deformation Mechanisms 313
Long-Range Dislocation Interactions 313
Orowan Stress 314
The Thermally Activated Detachment Model 315
Solution Hardening 316
Diffusional Point Defect Drag 317
8.3.4 Summary 317
8.4 Plastic Deformation During Fracture of Al2O3/Nb Sandwich Specimens 318
9 Intermetallic Alloys 322
9.1 Introduction 322
9.2 Ni3Al 325
9.2.1 Microscopic Observations and Dislocation Dynamics 325
9.2.2 Models of the Flow Stress Anomaly 328
9.3 -TiAl 331
9.3.1 Crystal Structure and Slip Geometry 332
9.3.2 Microscopic Observations 333
Room Temperature 333
High Temperatures 338
9.3.3 Macroscopic Deformation Parameters 340
9.3.4 Deformation Mechanisms 342
Room Temperature up to About 430C 343
Flow Stress Anomaly 346
9.3.5 Summary 349
9.4 NiAl 349
9.4.1 Crystal Structure and Slip Geometry 349
9.4.2 Microscopic Observations 350
9.4.3 Macroscopic Deformation Parameters 355
9.4.4 Deformation Mechanisms 357
Room Temperature 357
High Temperatures 358
9.4.5 Summary 364
9.5 FeAl 364
9.5.1 Microscopic Observations 364
9.5.2 Macroscopic Deformation Parameters 369
9.5.3 Deformation Mechanisms 371
Room Temperature 371
Flow Stress Anomaly 372
High-Temperature Range 376
9.5.4 Summary 377
9.6 Molybdenum Disilicide 378
9.6.1 Crystal Structure and Slip Geometry 378
9.6.2 Microscopic Observations 379
Deformation Along "426830A 201 "526930B 379
Deformation Along "426830A 110 "526930B 383
Stacking Faults 387
9.6.3 Macroscopic Deformation Parameters 389
9.6.4 Deformation Mechanisms 392
Low Temperatures 393
Flow Stress Anomaly 395
High-Temperature Range 398
9.6.5 Summary 398
9.7 Conclusions on Intermetallics 399
10 Quasicrystals 402
10.1 Structure of Quasicrystals 403
10.1.1 Quasicrystals with Icosahedral Symmetry 405
10.1.2 Quasicrystals with Decagonal Symmetry 407
10.2 Defects in Quasicrystals 409
10.2.1 Vacancies 409
10.2.2 Phason Defects 409
10.2.3 Dislocations 412
10.3 Microscopic Observations of Dislocations 417
10.3.1 i-Al–Pd–Mn 417
Transmission Electron Microscopy of Deformed Specimens 417
In situ Straining Experiments in an High-Voltage Electron Microscope 424
10.3.2 d-Al–Ni–Co 431
10.4 Macroscopic Deformation Parameters 440
10.4.1 i-Al–Pd–Mn 441
10.4.2 d-Al–Ni–Co 447
10.5 Mechanisms of Dislocation Motion and Plastic Deformation 449
10.5.1 Glide or Climb Motion of Dislocations 450
10.5.2 Components of the Flow Stress 452
10.5.3 Formation of Phason Faults 452
10.5.4 Long-Range Dislocation Interactions 454
10.5.5 Activation Parameters of Plastic Deformation 455
10.5.6 Friction Mechanisms of Dislocation Motion 457
10.5.7 Dislocation Kinetics in the High-Temperature Range 462
10.5.8 The Climb-Exchange Model 464
10.6 Conclusions on Quasicrystals 468
11 Conclusion 471
List of Abbreviations and Symbols 471
List of Video Clips 478
References 482
Index 1
Dislocation Dynamics During Plastic Deformation 6
Root 6
Part I General Properties of Dislocation Motion 14
1 Introduction 15
1.1 Theoretical Yield Strength 16
1.2 Plastic Shear by the Motion of Dislocations 17
2 Experimental Methods 22
2.1 Macroscopic Deformation Tests 22
2.2 Stress Pulse Double Etching Technique 27
2.3 Transmission Electron Microscopy 29
2.4 In Situ Straining Experiments in the Transmission Electron Microscope 31
2.5 Other Methods 37
2.5.1 X-Ray Topography In Situ Deformation Experiments 38
2.5.2 Surface Studies of Slip Lines 38
2.5.3 Internal Friction 40
2.5.4 Nuclear Magnetic Resonance 44
3 Properties of Dislocations 46
3.1 Geometric Properties 46
3.1.1 Burgers Vector 46
3.1.2 Glide and Climb Motion of a Dislocation 48
3.1.3 Relation Between Dislocation Motion and Plastic Strain and Strain Rate 50
3.2 Elastic Properties of Dislocations 51
3.2.1 Stress Fields of Straight Dislocations 52
3.2.2 Dislocation Energy 54
3.2.3 Forces on Dislocations 58
3.2.4 Interaction Between Parallel Dislocations 61
3.2.5 Interaction Between Nonparallel Dislocations 63
3.2.6 Elastic Interaction Between Dislocations and Elastic Inclusions 65
3.2.7 Bowed-Out Dislocations 68
3.3 Dislocations in Crystals 76
3.3.1 Selection of Burgers Vectors 77
3.3.2 Stacking Faults and Partial Dislocations 77
3.3.3 Twins 81
3.3.4 Antiphase Boundaries 82
4 Dislocation Motion 84
4.1 Thermally Activated Overcoming of Barriers 85
4.2 Lattice Friction 89
4.2.1 Peierls–Nabarro Model 90
4.2.2 Double-Kink Model 94
Elastic Properties of Kinks 94
Kinks in Thermal Equilibrium 96
Thermally Activated Motion of Kinks 97
Double-Kink Nucleation at High Stresses 99
Dislocation Velocity in the Range of Double-Kink Nucleation 101
4.2.3 Characteristics and Experimental Evidence of the Double-Kink Model 103
4.3 Slip and Cross Slip 104
4.4 The Locking–Unlocking Mechanism 110
4.5 Overcoming of Localized Obstacles 112
4.5.1 Friedel Statistics 114
4.5.2 Mott Statistics 121
4.6 Transition from the Double-Kink Mechanism to the Overcoming of Localized Obstacles 124
4.7 Overcoming of Extended Obstacles 127
4.8 Dislocation Intersections 137
4.9 Dislocation Motion at High Velocitiesand Low Temperatures 140
4.10 Dislocation Climb 143
4.10.1 Point Defect Equilibrium Concentrations 143
4.10.2 Climb Forces 145
Force Required for Athermal Climb 145
Applied Climb Forces 146
4.10.3 Emission- or Absorption-controlled Climb 148
4.10.4 Diffusion-controlled Climb 151
4.10.5 Jog Dragging 152
4.11 Drag Forces due to Point Defect Atmospheres 154
4.12 Dynamic Laws of Dislocation Mobility 161
5 Dislocation Kinetics, Work-Hardening, and Recovery 166
5.1 Dislocation Kinetics 166
5.1.1 Models of Dislocation Generation 167
5.1.2 Experimental Evidence of Dislocation Generation 173
5.1.3 Dislocation Immobilization and Annihilation 177
5.2 Work-Hardening and Recovery 182
5.2.1 Work-Hardening Models 183
5.2.2 Thermal and Athermal Componentsof the Flow Stress 191
5.2.3 Experimental Determinationof the Stress Components 198
5.2.4 Steady State Deformation 203
5.3 Plastic Instabilities 207
Part II Dislocation Motion in Particular Materials 213
Comments on the Video Sequences Available in the Internet 214
6 Semiconductors 216
6.1 Crystal Structure and Slip Geometry 216
6.2 Microscopic Observations 218
6.3 Dislocation Dynamics 222
6.4 Recombination-enhanced Dislocation Mobility 226
6.5 Macroscopic Deformation Properties 227
6.6 Summary 229
7 Ceramic Single Crystals 230
7.1 Alkali Halides 230
7.1.1 Crystal Structure and Slip Geometry 231
7.1.2 Dislocation Dynamics 232
7.1.3 Macroscopic Deformation Properties 232
7.1.4 Summary 238
7.2 Magnesium Oxide 240
7.2.1 Microscopic Observations 240
7.2.2 Statistics of Overcoming Localized Obstacles 243
7.2.3 Kinematics of Overcoming Localized Obstacles 248
7.2.4 Dislocation Dynamics 251
7.2.5 Macroscopic Deformation Properties and Discussion 252
7.2.6 Dislocations in the Plastic Zone of a Crack 258
7.2.7 Summary 261
7.3 Zirconia Single Crystals 262
7.3.1 Crystal Structure and Slip Geometry of ZrO2–Y2O3 alloys 262
7.3.2 Microscopic Observations in Cubic ZrO2 263
7.3.3 Dislocation Dynamics in Cubic ZrO2 269
7.3.4 Macroscopic Deformation Properties of Cubic ZrO2 270
7.3.5 Deformation Mechanisms 272
The Athermal Stress Component 272
Elastic Interactions Between Dislocations and Point Defects 274
Precipitation Hardening 275
The Peierls Mechanism 276
Formation of Solute Atmospheres Around Dislocations 277
Recovery Controlled Deformation at High Temperatures 279
7.3.6 Summary of Cubic ZrO2 282
7.3.7 Tetragonal ZrO2 282
Microstructure 283
Ferroelastic Deformation 283
Plastic Deformation 285
Partially Stabilized Zirconia 287
Summary of Tetragonal Zirconia 289
8 Metallic Alloys 290
8.1 Precipitation Hardened Aluminium Alloys 290
8.1.1 Al–Zn–Mg 291
8.1.2 Al–Ag 294
8.1.3 Al–Li 296
8.1.4 Summary 302
8.2 Dislocation Generation in Metals 302
8.3 Oxide Dispersion Strengthened Materials 306
8.3.1 Microscopic Observations in Oxide Dispersion Strengthened Alloys 307
8.3.2 Macroscopic Deformation Properties 312
8.3.3 Deformation Mechanisms 313
Long-Range Dislocation Interactions 313
Orowan Stress 314
The Thermally Activated Detachment Model 315
Solution Hardening 316
Diffusional Point Defect Drag 317
8.3.4 Summary 317
8.4 Plastic Deformation During Fracture of Al2O3/Nb Sandwich Specimens 318
9 Intermetallic Alloys 322
9.1 Introduction 322
9.2 Ni3Al 325
9.2.1 Microscopic Observations and Dislocation Dynamics 325
9.2.2 Models of the Flow Stress Anomaly 328
9.3 -TiAl 331
9.3.1 Crystal Structure and Slip Geometry 332
9.3.2 Microscopic Observations 333
Room Temperature 333
High Temperatures 338
9.3.3 Macroscopic Deformation Parameters 340
9.3.4 Deformation Mechanisms 342
Room Temperature up to About 430C 343
Flow Stress Anomaly 346
9.3.5 Summary 349
9.4 NiAl 349
9.4.1 Crystal Structure and Slip Geometry 349
9.4.2 Microscopic Observations 350
9.4.3 Macroscopic Deformation Parameters 355
9.4.4 Deformation Mechanisms 357
Room Temperature 357
High Temperatures 358
9.4.5 Summary 364
9.5 FeAl 364
9.5.1 Microscopic Observations 364
9.5.2 Macroscopic Deformation Parameters 369
9.5.3 Deformation Mechanisms 371
Room Temperature 371
Flow Stress Anomaly 372
High-Temperature Range 376
9.5.4 Summary 377
9.6 Molybdenum Disilicide 378
9.6.1 Crystal Structure and Slip Geometry 378
9.6.2 Microscopic Observations 379
Deformation Along "426830A 201 "526930B 379
Deformation Along "426830A 110 "526930B 383
Stacking Faults 387
9.6.3 Macroscopic Deformation Parameters 389
9.6.4 Deformation Mechanisms 392
Low Temperatures 393
Flow Stress Anomaly 395
High-Temperature Range 398
9.6.5 Summary 398
9.7 Conclusions on Intermetallics 399
10 Quasicrystals 402
10.1 Structure of Quasicrystals 403
10.1.1 Quasicrystals with Icosahedral Symmetry 405
10.1.2 Quasicrystals with Decagonal Symmetry 407
10.2 Defects in Quasicrystals 409
10.2.1 Vacancies 409
10.2.2 Phason Defects 409
10.2.3 Dislocations 412
10.3 Microscopic Observations of Dislocations 417
10.3.1 i-Al–Pd–Mn 417
Transmission Electron Microscopy of Deformed Specimens 417
In situ Straining Experiments in an High-Voltage Electron Microscope 424
10.3.2 d-Al–Ni–Co 431
10.4 Macroscopic Deformation Parameters 440
10.4.1 i-Al–Pd–Mn 441
10.4.2 d-Al–Ni–Co 447
10.5 Mechanisms of Dislocation Motion and Plastic Deformation 449
10.5.1 Glide or Climb Motion of Dislocations 450
10.5.2 Components of the Flow Stress 452
10.5.3 Formation of Phason Faults 452
10.5.4 Long-Range Dislocation Interactions 454
10.5.5 Activation Parameters of Plastic Deformation 455
10.5.6 Friction Mechanisms of Dislocation Motion 457
10.5.7 Dislocation Kinetics in the High-Temperature Range 462
10.5.8 The Climb-Exchange Model 464
10.6 Conclusions on Quasicrystals 468
11 Conclusion 471
List of Abbreviations and Symbols 471
List of Video Clips 478
References 482
Index 505

"Part I General Properties of Dislocation Motion (p. 2-4)

1 Introduction

The properties of crystalline solids can be classified into two groups. To the first one belong, for example, the elastic properties or the occurrence of X-ray diffraction patterns. These phenomena are controlled by the regular periodic structure of the crystal lattice. The second group involves properties like diffusion or the mechanical strength. Though these phenomena are also influenced by the regular crystal structure and its binding properties, they are essentially controlled by the defects in the regular arrangement of the atoms and may be called structure sensitive properties, as was introduced by Smekal [1].

The crystal defects are classified according to their extension in space into zero, one, two, and three-dimensional defects. Zero-dimensional defects or point defects include single missing atoms called vacancies, interstitial atoms, and substitutionally or interstitially incorporated foreign atoms like impurities. One-dimensional defects occur if the regular coordination of atoms is disturbed along a line.

These defects are called dislocations being the topic of this book. Two-dimensional defects are grain and phase boundaries while three-dimensional ones are larger precipitates or inclusions. Since the movement of dislocations is influenced by all types of defects, it turns out to be a very complex process. In the following section, it is shown that shearing a crystalline solid along a plane as a whole requires a high stress, which exceeds the measured strengths of materials by several orders of magnitude. Afterwards, in Sect. 1.2, dislocations are introduced.

Their motion through the crystal lattice allows the shearing in small steps, yielding realistic values of the mechanical strength. Part I of the book treats the general features of the dynamic dislocation behavior. At first, an outline of the experimental methods is given in Chap. 2. As a basis for understanding the dynamics, the geometric and elastic dislocation properties as well as the structure of dislocations in real crystals are reviewed in Chap. 3 before the dislocation motion itself is treated in Chap. 4.

Chapter 5 is concerned with the kinetic processes of dislocation generation, immobilization and annihilation. Part II is devoted to the dislocation motion in particular material classes, that is, to semiconductors in Chap. 6, ceramic single crystals (Chap. 7), metals (Chap. 8), intermetallic alloys (Chap. 9), and finally to quasicrystals (Chap. 10). In these chapters, particular dislocation processes are discussed in more detail and, whenever possible, they are illustrated by video sequences."